prudential policy for peggers · ity pegging the nominal exchange rate creates a pecuniary...
TRANSCRIPT
Prudential Policy For Peggers
Stephanie Schmitt-Grohe∗ Martın Uribe†
June 13, 2012First draft January 3, 2012
Abstract
This paper shows that in a small open economy with downward nominal wage rigid-ity pegging the nominal exchange rate creates a pecuniary externality. The externalitycauses unemployment, overborrowing, and depressed consumption. Ramsey optimal
capital control policy is characterized and shown to be prudential. For it taxes capitalinflows in good times and subsidizes external borrowing in bad times. Under plausible
calibrations, this type of macro prudential policy is shown to lower the average unem-ployment rate by 10 percentage points, to reduce average external debt by 10 to 50
percent, and to increase welfare by over 9 percent of consumption per period.
JEL Classifications: F41, E31, E62.Keywords: Currency pegs, downward wage rigidity, capital controls, pecuniary externality.
∗Columbia University, CEPR, and NBER. E-mail: [email protected].†Columbia University and NBER. E-mail: [email protected].
1 Introduction
Fixed-exchange rate arrangements are often part of broader economic reform programs that
include liberalization of international capital flows. For small emerging economies, such a
policy combination has been a mixed blessing. A case in point is the European currency
union, which imposes capital account liberalization as a prerequisite for admission. Figure 1
displays the average current-account-to-GDP ratio, an index of nominal hourly wages in
Euros, and the rate of unemployment for a group of peripheral European countries that
are either on or pegging to the Euro over the period 2000 to 2011. In the early 2000s,
these peripheral members of the eurozone enjoyed large capital inflows, which through their
expansionary effect on domestic absorption, led to sizable appreciations in hourly wages.
With the onset of the global recession in 2008, however, capital inflows dried up and aggregate
Figure 1: Boom-Bust Cycle in Peripheral Europe: 2000-2011
2002 2004 2006 2008 20106
7
8
9
10
11
12
13
14
Perc
ent
Date
Unemployment Rate
2002 2004 2006 2008 201050
60
70
80
90
100
110
Index, 200
8 =
100
Date
Labor Cost Index, Nominal
2002 2004 2006 2008 2010−14
−12
−10
−8
−6
−4
−2
Perc
ent
Date
Current Account / GDP
Data Source: Eurostat. Data represents arithmetic mean of Bulgaria, Cyprus, Estonia,
Greece, Lithuania, Latvia, Portugal, Spain, Slovenia, and Slovakia.
demand collapsed. At the same time nominal wages remained at the level they had achieved
at the peak of the boom. The combination of depressed levels of aggregate demand and high
nominal wages was associated with a massive increase in involuntary unemployment. In
turn, local monetary authorities were unable to reduce real wages via a devaluation because
of their commitment to the currency union.
This narrative evokes several interrelated questions. One is what is the connection be-
tween capital mobility and the economic performance of fixed exchange rate regimes. An-
other is whether emerging-country peggers might be better off imposing capital controls.
And, if so, whether optimal capital controls are prudential in nature. The goal of this paper
is to address these questions in the context of a dynamic, stochastic, optimizing model of an
1
emerging economy. The central counterfactual situation considered in our analysis, i.e., the
imposition of capital controls, serves as a way to highlight the costs imposed by the current
institutional arrangement in the European Union that insists on free capital mobility. The
main point that emerges from our analysis is that the combination of free capital mobility
and currency pegs is highly deleterious for peripheral members of the union.
Our theoretical laboratory is the Schmitt-Grohe and Uribe (2011a) model of an open
economy with tradable and nontradable goods, downward nominal wage rigidity and a fixed
exchange rate. The model economy is driven by exogenous and stochastic disturbances to the
endowment of tradable goods and to the country interest rate. We show that in the context
of this model, the combination of downward nominal wage rigidity, a fixed exchange rate, and
free capital mobility creates a negative pecuniary externality. The nature of the externality
identified in the present paper is as follows. Expansions in aggregate demand drive up wages,
putting the economy in a vulnerable situation. For in the contractionary phase of the cycle,
downward nominal wage rigidity and a fixed exchange rate prevent real wages from falling
to the level consistent with full employment. Agents understand this mechanism, but are
too small to internalize the fact that their individual expenditure decisions collectively cause
inefficiently large increases in wages during expansions, which exacerbate unemployment
during contractions.
The existence of the pecuniary externality creates a rationale for government intervention.
We focus on capital controls as a second-best instrument. In particular, we assume that the
government levies a proportional tax (subsidy) on net external debt holdings. The tax
is equivalent to an interest rate markup on net foreign liabilities. We then characterize
analytically and numerically optimal capital control policy under commitment. We show
that the Ramsey-optimal tax on external debt is positive on average and highly procyclical.
Thus, the optimal capital control policy is prudential in nature, as it restricts capital inflows
in good times and subsidizes external borrowing in bad times.
In our model, a benevolent government has an incentive to levy taxes on external debt
during expansions as a way to limit nominal wage growth. Moderating wage growth dur-
ing booms helps ameliorate the unemployment problem caused by downward wage rigidity
during contractions. In turn, capital controls affect wage growth through their effect on
the aggregate absorption of tradable goods. In our small open economy, consumption of
tradables acts as a shifter of the demand for nontradables. As a result, the government
can indirectly affect employment in the nontraded sector by manipulating the intertempo-
ral price of tradables (the interest rate) via capital controls. Thus, the government in a
fixed-exchange-rate economy determines the optimal capital control policy as the solution to
a trade off between intertemporal distortions (caused the capital controls themselves) and
2
static distortions (caused by downward real wage rigidity).
Importantly, the optimal capital control policy implied by our model does not belong to
the class of beggar-thy-neighbor policies. For it does not seek to increase foreign demand
for domestic goods during crises. On the contrary, the optimal capital control policy in
our model is one in which during crises the government subsidizes domestic absorption of
tradable goods, thereby discouraging exports. The reason why the government has incentives
to stimulate imports during downturns is that greater domestic absorption of tradables
increases demand for nontradables, thereby reducing unemployment in the nontraded sector.
Versions of the model calibrated to Argentina, Greece, and Spain show that the optimal
capital control policy achieves significant reductions in unemployment (about 10 percentage
points) and that the welfare gains from macro prudential policy are large, amounting to over
9 percent of consumption per period.
Further, we find that free capital mobility induces peggers to overborrow. Specifically,
for our baseline calibration, the average external debt-to-output ratio in the economy with
free capital mobility is more than twice as large as the one induced under optimal capital
controls.
Capital controls are not the only instruments through which the policymaker can address
the inefficiencies arising from the combination of a currency peg and downward nominal wage
rigidity. Elsewhere, we have shown that the first-best allocation can be achieved by means of
optimal labor or consumption subsidies (Schmitt-Grohe and Uribe, 2011a, 2012b). A natural
question is then why bother characterizing optimal capital controls, if, after all, they achieve
only a second-best allocation. The reason is that policymakers may find that capital controls
is the only instrument that they can implement in practice. The use of labor subsidies to
achieve the first best may be difficult from a political point of view. In Schmitt-Grohe
and Uribe (2011a, 2012b) we show that the labor subsidy scheme that implements the first
best inherits the stochastic properties of the underlying shocks, which in emerging countries
like those in the periphery of Europe, are highly volatile. Thus the optimal labor subsidy
scheme would require large variations in wage subsidies at a quarterly frequency. This may
be highly problematic in light of the fact that the institutional arrangements (especially the
legislative process) that govern the determination of income taxes is highly inertial, making
large swings in labor subsidies on a quarter-to-quarter basis unrealistic. By contrast, capital
controls can be politically portrayed as taxes on foreign speculators. As a result the executive
branch of the government typically is given much more leeway to set capital-inflow taxes at
business-cycle frequency.
In the case of Europe, all three policy options for addressing the inefficiencies brought
about by downward nominal wage rigidity, namely devaluation, labor/production subsidies,
3
and capital controls, are limited by existing supranational arrangements. If peripheral Eu-
rope is to achieve stability central aspects of these arrangements are likely to change. It
is therefore of interest to fully characterize the business-cycle implications of each of these
three policy alternatives. The contribution of the current paper is to investigate the poten-
tial benefits of moving away from free capital mobility toward a policy of optimally designed
capital controls.
We view our work as most closely related to the Mundellian literature on the trilemma
of international finance, according to which a country cannot have at the same time a
fixed exchange rate, free capital mobility, and an independent interest rate policy. (For a
recent treatment, see Obstfeld et al., 2010.) We present an explicit articulation of this view
in the context of a dynamic, optimizing model of a small open economy with downward
nominal wage rigidity. We take a fixed exchange rate regime as a given, because we wish to
understand the policy options available to the peripherical members of the eurozone short
of breaking away from the common currency arrangement. In our model economy, the
benevolent government has an incentive to vary the effective interest rate (through capital
controls) as a way to insulate the nontraded sector from external shocks. The existing
theoretical literature on optimal capital controls based on the trilemma of international
finance is quite informal and reduced form. By contrast, the building blocks of our theoretical
framework are welfare maximizing households, profit maximizing firms, and a benevolent
government operating in a dynamic and uncertain environment. Consequently, our model,
once calibrated to capture key elements of actual emerging economies, allows us to derive
sharp predictions about the welfare-maximizing capital control process and its associated
real allocation.
A second strand of the related literature stresses financial distortions, such as collat-
eral constraints on external borrowing as a rationale for capital controls (Auernheimer and
Garcıa-Saltos, 2000; Uribe, 2006, 2007; Lorenzoni, 2008; Korinek, 2010; Benigno et al., 2011;
and Bianchi, 2011). A third line of work is based on the classical trade theoretic argument
that large countries can affect the interest rate, or the intertemporal price of consumption
(e.g., Obstfeld and Rogoff, 1996 section 1.4, Schmitt-Grohe and Uribe, 2012a section 4.4,
and Costinot et al., 2011). As a result, governments of large countries have incentives to
apply capital controls as a means to induce households to internalize the country’s market
power in financial markets. Our theory of capital controls is distinct from the above two in
that it does not assume the existence of collateral constraints or market power in financial
markets.
The remainder of the paper is organized in eight sections. Section 2 embeds capital
controls into a small open economy model with downward nominal wage rigidity and a
4
fixed-exchange rate. Section 3 characterizes optimal capital control policy under commit-
ment. It shows analytically that the optimal capital-control policy is prudential. Section 4
calibrates the model to the Argentine economy. It analyzes quantitatively the behavior of
the economy with and without capital controls undergoing a boom-bust cycle. Section 5
presents the effects of optimal capital controls on first and second unconditional moments
of key macroeconomic aggregates. Section 6 identifies and quantifies overborrowing induced
by the combination of a currency peg and downward nominal wage rigidity. Section 7 in-
vestigates the welfare losses due to free capital mobility in fixed exchange rate economies.
Section 8 shows that our main results are robust to using data from Greece and Spain in the
econometric estimation of the exogenous driving forces. Section ?? concludes.
2 An Open Economy With Downward Wage Rigidity
We embed capital controls into the small open economy model with downward nominal wage
rigidity developed in Schmitt-Grohe and Uribe (2011a). We assume that the nominal wage
rate, denoted Wt, must satisfy the following restriction
Wt ≥ γWt−1, (1)
where γ is a nonnegative parameter governing the degree of downward nominal wage rigidity.
The larger is γ, the more stringent is the downward rigidity in nominal wages. In Schmitt-
Grohe and Uribe (2011a), we present empirical evidence suggesting that γ is close to unity.
Throughout the present analysis, we assume that the central bank pegs the nominal
exchange rate. Specifically, letting Et denote the domestic-currency price of one unit of
foreign currency, we impose
Et = E (2)
for all t, where E is a positive constant. The combination of a fixed-exchange-rate regime
and downward nominal wage rigidity introduces a real rigidity. Specifically, the wage rate
in terms of foreign currency, denoted wt ≡ Wt/Et is downwardly rigid. This rigidity makes
the economy vulnerable to any shock that requires a fall in real wages. The inability of the
real wage to fall will in general cause unemployment and therefore a loss of welfare.
The inefficiency introduced by the combination of downward nominal wage rigidity and a
fixed exchange rate, opens the door to welfare-improving fiscal policy. In the present inves-
tigation, we study the extent to which capital controls can help ameliorate this inefficiency.
We model capital controls as a proportional tax on gross capital inflows.
The model features two types of good, tradables and nontradables. Tradable output is
5
exogenous and stochastic, while nontraded output is produced with labor services. The econ-
omy is driven by two exogenous shocks. One is the endowment of tradables just described.
The second shock emerges from the assumption that the interest rate charged to the small
open economy in international financial markets is exogenous and stochastic.
2.1 Households
The economy is populated by a large number of identical households with preferences de-
scribed by the utility function
E0
∞∑
t=0
βtU(ct), (3)
where ct denotes consumption. The period utility function U is assumed to be strictly
increasing and strictly concave and the parameter β, denoting the subjective discount factor
resides in the interval (0, 1). The symbol Et denotes the mathematical expectations operator
conditional upon information available in period t. The consumption good is a composite of
tradable consumption, cTt , and nontradable consumption, cN
t . The aggregation technology is
of the form
ct = A(cTt , cN
t ), (4)
where A is an increasing, concave, and linearly homogeneous function.
We assume full liability dollarization. Specifically, households have access to a one-
period, internationally traded, state non-contingent bond denominated in tradables. We let
dt denote the level of debt assumed in period t−1 and due in period t and rt the interest rate
on debt held between periods t and t+1. The sequential budget constraint of the household
is given by
cTt + ptc
Nt + dt = (1 + τ y
t )[yTt + wtht + φt] +
dt+1(1 − τ dt )
1 + rt
, (5)
where pt ≡ PNt /P T
t denotes the relative price of nontradables in terms of tradables, with
PNt and P T
t , denoting, respectively, the nominal prices of nontradables and tradables. We
assume that the law of one price holds for tradables. Specifically, we let P T ∗
t denote the
foreign currency price of tradables and Et the nominal exchange rate, defined as the domestic-
currency price of one unit of foreign currency. Then, the law of one price implies that
P Tt = P T ∗
t Et.
We assume that the foreign-currency price of tradables is constant and normalized to unity,
P T ∗
t = 1.
6
The variable τ dt denotes the tax rate on debt acquired in period t. For each unit of
tradable good that the household promises to pay in period t+1, it receives (1− τ dt )/(1+ rt)
units in period t. The government intervention in the international financial market alters
the effective gross interest rate paid by the household from 1 + rt to (1 + rt)/(1 − τ dt ). The
rate τ dt can take positive or negative values. When it is positive, the government discourages
borrowing by raising the effective interest rate. In this case, we say that the government
imposes capital controls. On the other hand, when τ dt is negative, the government subsidizes
international borrowing by lowering the effective interest rate. As we will see shortly, a
benevolent government will make heavy use of cyclical adjustments in capital controls to
stabilize consumption and employment.
The variable τ yt denotes a proportional income subsidy rate (tax rate if negative) deter-
mined by the government. It serves as a channel for the government to rebate the fiscal
revenues created by the imposition of capital controls. Because all of the components of
nonfinancial individual income are taken as exogenous by the household, the income tax
τ yt is nondistorting. Specifically, nonfinancial household income is given by yT
t + wtht + φt,
where ht denotes hours worked and φt denotes profits from the ownership of firms. House-
holds supply inelastically h hours to the labor market each period. However, because of the
presence of downward nominal wage rigidity, they may not be able to sell all of the hours
supplied. As a result, households take employment, ht ≤ h, as exogenously given.
Households are assumed to be subject to the following debt limit, which prevents them
from engaging in Ponzi schemes.
dt+1 ≤ d, (6)
where d denotes the natural debt limit. Households choose contingent plans {ct, cTt , cN
t , dt+1}
to maximize (3) subject to (4)-(6) taking as given wt, ht, φt, yTt , rt, τ d
t , τ yt , and pt. The
optimality conditions associated with this problem are (4)-(6) and
A2(cTt , cN
t )
A1(cTt , cN
t )= pt, (7)
λt = U ′(ct)A1(cTt , cN
t ),
λt(1 − τ dt )
1 + rt
= βEtλt+1 + µt,
µt ≥ 0,
µt(dt+1 − d) = 0,
where λt and µt denote the Lagrange multipliers associated with (5) and (6), respectively.
7
Figure 2: Pecuniary Externality
h
p
A2(cT
0, F (h))
A1(cT
0, F (h))
A2(cT
boom, F (h))
A1(cT
boom, F (h))
W0/EF ′(h)
Wboom/EF ′(h)
h
A
BC
Dp0
pbust
pboom
hbust
Equation (7) describes the demand for nontradables as a function of the relative price
of nontradables, pt, and the level of tradable absorption, cTt . Given cT
t , the demand for
nontradables is strictly decreasing in pt. This is a consequence of the assumptions made
about the aggregator function A. It reflects the fact that as the relative price of nontradables
increases, households tend to consume relatively less nontradables. The demand function
for nontradables is depicted in figure 2 as a downward sloping solid line. (Notice that in the
figure, the demand function is plotted in the space (ht, pt), rather than in the space (cNt , pt).
As will become clear shortly, we are jumping ahead and using the fact that under market
clearing in the nontraded sector, cNt = F (ht) at all times. We refer to the depicted locus as the
demand function for nontradables, even though strictly speaking it is not.) An increase in the
absorption of tradables shifts the demand schedule up and to the right, reflecting normality.
This shift is shown with a dashed downward sloping line in figure 2, for an increase in traded
consumption from cT0 to cT
boom. It follows that absorption of tradables can be viewed as a
8
shifter of the derived demand for labor. Of course, cTt is itself an endogenous variable, which
is determined simultaneously with all other endogenous variables of the model.
2.2 Firms
Nontraded output is produced by perfectly competitive firms. Each firm operates a produc-
tion technology given by F (ht), which uses labor services as the sole input. The function F
is assumed to be strictly increasing and strictly concave. Firms choose the amount of labor
input to maximize profits, given by
φt ≡ ptF (ht) − wtht.
The optimality condition associated with this problem is
ptF′(ht) = wt.
This condition represents the supply of nontradable goods. It is depicted with a solid upward
sloping line in the space (h, p) in figure 2. Ceteris paribus, the higher is the relative price of
the nontraded good, the higher is the demand for labor and therefore the larger the supply of
nontradable goods. Also, all other things equal, the higher is the labor cost wt, the smaller
are the demand for labor and the supply of nontradables at each level of the relative price
pt. Figure 2 displays with a broken upward sloping line the shift in the supply schedule
that results from an increase in the nominal wage rate from W0 to Wboom > W0, holding the
nominal exchange rate constant at E.
2.3 Closure of the Labor Market
The following three conditions must hold at all times:
wt ≥ γwt−1,
ht ≤ h,
and
(ht − h)(wt − γwt−1) = 0.
The first two constraints were already introduced. The third is a slackness condition stating
that whenever there is underemployment the lower bound on wages must bind, and that
whenever this lower bound is not binding, the labor market must operate at full employment.
9
2.4 The Government
The government imposes a proportional tax (subsidy) on debt, τ dt , and a proportional subsidy
(tax) on income, τ yt . Given τ d
t , whose determination we will discuss shortly, the government
sets income subsidies to balance the budget period by period. Specifically, τ yt satisfies
τ yt (yT
t + wtht + φt) = τ dt
dt+1
1 + rt
2.5 Competitive Disequilibrium Dynamics
Because product prices are assumed to be fully flexible, the market for nontraded goods
must clear at all times. That is, the condition
cNt = F (ht)
holds for all t. Combining this condition, the household’s budget constraint, the government’s
budget constraint, and the definition of firms’ profits, we obtain the following market-clearing
condition for traded goods:
cTt + dt = yT
t +dt+1
1 + rt
. (8)
The complete set of conditions describing the competitive disequilibrium dynamics is then
given by (8) and
P (cTt , ht)F
′(ht) = wt, (9)
ht ≤ h, (10)
wt ≥ γwt−1, (11)
dt+1 ≤ d, (12)
λt = U ′(A(cTt , F (ht)))A1(c
Tt , F (ht)), (13)
λt(1 − τ dt )
1 + rt
= βEtλt+1 + µt, (14)
µt ≥ 0, (15)
µt(dt+1 − d) = 0, (16)
(ht − h)(wt − γwt−1) = 0, (17)
τ yt = τ d
t
dt+1/(1 + rt)
yTt + P (cT
t , ht)F (ht), (18)
10
where
P (cTt , ht) ≡
A2(cTt , F (ht))
A1(cTt , F (ht))
denotes the relative price of nontradables in terms of tradables expressed as a function of
consumption of tradables and employment.
3 Optimal Capital Controls
The combination of downward nominal wage rigidity and a currency peg creates a negative
pecuniary externality. The nature of this externality is that in periods of economic expansion,
elevated demand for nontradables drives real wages up placing the economy in a vulnerable
situation. For in the contractionary phase of the cycle, downward nominal wage rigidity and
the currency peg hinder the downward adjustment of real wages, causing unemployment.
Individual agents understand this mechanism, but are too small to internalize the fact that
their own expenditure choices collectively exacerbate disruptions in the labor market.
The pecuniary externality can be visualized in figure 2. The initial position of the econ-
omy is at point A, where the labor market is operating at full employment, ht = h. In
response to a positive external shock, traded absorption increases from cT0 to cT
boom causing
the demand function to shift up and to the right. If nominal wages stayed unchanged, the
new intersection of the demand and supply schedules would occur at point B. However, at
that point, employment would exceed the available supply of labor h. The excess demand for
labor drives up the nominal wage from W0 to Wboom causing the supply of nontradables to
shift up and to the left. The new intersection of the demand and supply schedules occurs at
point C , where full employment is restored and the excess demand for labor has disappeared.
Suppose now that the external shock fades away, and that, therefore, absorption of
tradables goes back to its original level cT0 . The decline in cT
t shifts the demand schedule
back to its original position. However, the economy does not immediately return to point A,
because, due to downward nominal wage rigidity, the nominal wage stays at Wboom and, as
a result, the supply schedule does not move. The new intersection is at point D. There, the
economy suffers involuntary unemployment equal to h − hbust. Over time, the economy will
return to point A. However, the convergence is inefficient because it features unemployment
throughout. Consequently, the government has an incentive to prudentially regulate capital
flows to curb the initial expansion in tradable consumption in response to positive external
shocks. Such policy would dampen the initial increase in nominal wages and in that way
mitigate the subsequent unemployment problem as the economy returns to its initial state.
In the present study, we focus on a second-best type of government intervention that
11
takes the form of capital controls. Specifically, we assume that the instruments available
to the government are the tax rate on debt τ dt and the income subsidy τ y
t . The latter tax
is merely used as a vehicle to rebate in a nondistorting fashion the revenues generated by
capital controls. The government is assumed to be benevolent and to be endowed with full
commitment. We therefore refer to the fiscal authority as the Ramsey planner. It is worth
noting that the battery of fiscal instruments available to our Ramsey planner is limited to
capital controls, and, in particular, does not include wage-subsidy schemes in labor markets
afflicted by downward wage rigidity. Elsewhere (Schmitt-Grohe and Uribe, 2011a) we show
that appropriately designed wage subsidies can fully eliminate the distortions arising from
the combination of downward wage rigidity and a currency peg.
The Ramsey planner’s optimization problem consists in choosing a tax scheme {τ dt , τ y
t }
to maximize the household’s lifetime utility function (3) subject to the complete set of con-
ditions describing the competitive dynamics, equations (8)-(18). The strategy we follow to
characterize the Ramsey allocation is to drop conditions (13)-(18) from the set of constraints
of the Ramsey planner’s problem and then to show that the solution to this less constrained
problem satisfies the omitted constraints.
Accordingly, the Lagrangian of the less constrained Ramsey problem is given by
L = E0
∞∑
t=0
βt{
U(A(cTt , F (ht)))
+λct
[
yTt +
dt+1
1 + rt
− cTt − dt
]
+λpt
[
P (cTt , ht)F
′(ht) − wt
]
+λht
[
h − ht
]
+λwt [wt − γwt−1]
+λdt
[
d − dt+1
]}
,
where λct > 0, λh
t ≥ 0, λwt ≥ 0, λd
t ≥ 0, and λpt are Lagrange multipliers.
The first-order optimality conditions with respect to λct , λp
t , λht , λw
t , λdt , cT
t , ht, dt+1, wt,
and associated slackness conditions are, respectively, (8)-(12) and
U ′(A(cTt , F (ht))A1(c
Tt , F (ht)) = λc
t − λpt P1(c
Tt , ht)F
′(ht) (19)
U ′(A(cTt , F (ht))A2(c
Tt , F (ht))F
′(ht) = λht − λp
t [P2(cTt , ht)F
′(ht) + P (cTt , ht)F
′′(ht)] (20)
λct
(1 + rt)= βEtλ
ct+1
+ λdt (21)
12
λwt = βγEtλ
wt+1 + λp
t (22)
(ht − h)λht = 0 (23)
λwt (wt − γwt−1) = 0 (24)
(dt+1 − d)λdt = 0 (25)
We now show that allocations {cTt , ht, wt} that satisfy the optimality conditions of the
less constrained Ramsey problem, that is, conditions (8)-(12) and (19)-(25), also satisfy the
constraints that were omitted from the Ramsey problem, namely, conditions (13)-(18). To
see this, first pick λt to satisfy (13). Next, set µt = 0 for all t.1 It follows that (15) and
(16) are satisfied. Pick τ dt to satisfy (14). To ensure that the Ramsey policy is revenue
neutral, pick τ yt to satisfy (18). It remains to be shown that (17) is also implied by the set of
Ramsey optimality conditions. To see that this is the case, consider the following proof by
contradiction. Suppose, contrary to what we wish to show, that in the Ramsey allocation
ht < h and wt > γwt−1 at some date and state. Then, by (23) and (24), it must be the case
that λht = λw
t = 0. But then, by (20) and by the facts that P2(cTt , ht) < 0 and F ′′(ht) < 0,
we have that λpt > 0. This implication contradicts condition (22), which indicates that
λpt = −βγEtλ
wt+1
≤ 0 (recall that λwt ≥ 0).
From the arguments presented above, we have that the optimal capital control policy
must deliver tax rates on debt satisfying
τ dt = 1 − β(1 + rt)
EtU′(ct+1)A1(c
Tt+1, c
Nt+1)
U ′(ct)A1(cTt , cN
t ), (26)
where ct, cTt , and cN
t denote the Ramsey-optimal processes of consumption, consumption
of tradables, and consumption of nontradables, respectively.2 It follows from the above
expression that, all other things equal, capital controls are positive when the marginal utility
of tradables is expected to fall. That is, capital controls are more likely to be put into place
1Note that in states in which the Ramsey allocation calls for setting dt+1 < d, µt must be chosen to bezero. However, in states in which the Ramsey allocation yields dt+1 = d, µt need not be chosen to be zero. Inthese states, any positive value of µt could be supported in the decentralization of the Ramsey equilibrium.Of course, in this case, τd
t will depend on the chosen value of µt. In particular, τdt will be strictly decreasing
in the arbitrarily chosen value of µt and will be smaller than the one given in equation (26).2The Ramsey allocation can also be supported through consumption taxes. Specifically, assume that
instead of taxing external debt, the government taxes total consumption expenditures, cTt +ptc
Nt at the rate
τ ct−1, so that the after-tax cost of consumption in period t is (cT
t + ptcNt )(1 + τ c
t−1). The consumption taxrate is determined one period in advance. That is, in period t the government announces the tax rate onconsumption expenditures in period t + 1. One can show that the Ramsey allocation can be supported bya consumption-tax-rate process of the form 1 + τ c
t= (1 − τd
t)(1 + τ c
t−1), for any initial condition τ c
−1 > −1,where τd
t represents the Ramsey optimal tax rate on external debt given in equation (26).
13
when either total consumption or consumption of tradables or both are expected to grow.3
Conversely, all other things equal, the Ramsey fiscal authority loosens capital restrictions
when aggregate consumption or consumption of tradables or both are expected to decline.
It follows that the optimal capital control policy is essentially prudential, in the sense that
restrictions to capital inflows are imposed during the expansionary phase of the cycle and
loosened during the contractionary phase.
An implication of the previous analysis is that one can characterize the Ramsey allocation
as the solution to the following Bellman equation problem:
v(yTt , rt, dt, wt−1) = max
[
U(A(cTt , F (ht)) + βEtv(yT
t+1, rt+1, dt+1, wt)
]
(27)
subject to (8)-(12), where v(yTt , rt, dt, wt−1) denotes the value function of the representative
household. We exploit this formulation of the Ramsey problem in our numerical analysis.
We close this section by pointing out that the model with Ramsey optimal capital controls
is equivalent to one in which a benevolent government chooses the level of external debt
and households cannot participate in financial markets but are hand-to-mouth agents. In
this formulation, households receive a transfer from the government each period and their
choice is limited to the allocation of expenditure between tradable and nontradable goods.
The government then chooses the aggregate level of external debt taking into account the
pecuniary externality created by the combination of downward nominal wage rigidity and a
currency peg.
4 Dynamics Under Optimal Capital Controls
We wish to characterize aggregate dynamics under optimal capital controls. Of particular
interest is to compare the model’s predictions with and without capital controls. Given
the complexity of the model, this question must be addressed using numerical methods.
Specifically, using a calibrated version of the model, we compare aggregate dynamics and
welfare associated with free capital mobility and with the optimal capital control policy.
We assume a CRRA form for the period utility function, a CES form for the aggregator
function, and an isoelastic form for the production function of nontradables:
U(c) =c1−σ − 1
1 − σ,
3Strictly speaking, the marginal utility of consumption of tradables is decreasing in total consumptiononly if the intertemporal elasticity of substitution is smaller than the intratemporal elasticity of substitution.
14
Table 1: Calibration
Parameter Value Descriptionγ 0.99 Degree of downward nominal wage rigidity (Schmitt-Grohe and Uribe, 2011a)σ 5 Inverse of intertemporal elasticity of consumption (Ostry and Reinhart, 1992)yT 1 Steady-state tradable outputh 1 Labor endowmenta 0.26 Share of tradables (Schmitt-Grohe and Uribe, 2011a)ξ 0.44 Intratemporal Elasticity of Substitution (Gonzalez Rozada et al., 2004)α 0.75 Labor share in nontraded sector (Uribe, 1997)β 0.9375 Quarterly subjective discount factor (Schmitt-Grohe and Uribe, 2011a)
Note. See Schmitt-Grohe and Uribe (2011a) for details.
A(cT , cN) =[
a(cT )1−1
ξ + (1 − a)(cN)1−1
ξ
]ξ
ξ−1
,
and
F (h) = hα.
We calibrate the model at a quarterly frequency. All parameter values are taken from
Schmitt-Grohe and Uribe (2011a) and are shown in table 1. The single most relevant pa-
rameter in our model is γ, governing the degree of downward nominal wage rigidity. In
Schmitt-Grohe and Uribe (2011a), we present empirical evidence suggesting that nominal
wages are downwardly rigid, and that our calibration of 0.99 for γ is conservative, in the
sense that the empirical evidence points to values of γ greater than 0.99.
We also borrow from earlier work (Schmitt-Grohe and Uribe, 2011a) the stochastic pro-
cess driving aggregate fluctuations in our economy. Specifically, we assume that tradable
output and the country interest rate, denoted rt, follow a bivariate, first-order, autoregres-
sive process of the form[
ln yTt
ln 1+rt
1+r
]
= A
[
ln yTt−1
ln 1+rt−1
1+r
]
+ νt, (28)
where νt is a white noise of order 2 by 1 distributed N(∅, Σν). The parameter r denotes
the deterministic steady-state value of rt. The country interest rate rt represents the rate at
which the country can borrow in international markets. In Schmitt-Grohe and Uribe (2011a),
we estimate the system (28) using Argentine data over the period 1983:Q1 to 2001:Q4. Our
OLS estimates of the matrices A and Σν and of the scalar r are
A =
[
0.79 −1.36
−0.01 0.86
]
; Σν =
[
0.00123 −0.00008
−0.00008 0.00004
]
; r = 0.0316.
15
We discretize the AR(1) process given in equation (28) using 21 equally spaced points for
ln yTt and 11 equally spaced points for ln(1 + rt)/(1 + r). For details, see Schmitt-Grohe and
Uribe (2011a).
We numerically approximate the equilibrium dynamics under the optimal capital control
policy by applying the method of value function iteration over a discretized state space.
The state of the economy in period t ≥ 0 consists of the exogenous variables yTt and rt, the
endogenous state dt, and the endogenous predetermined variable wt−1. The welfare of the
representative household under the optimal capital control policy can be approximated by
solving the functional equation (27) subject to (8)-(12).
Approximating the dynamics of the model economy under free capital mobility is compu-
tationally more demanding than doing so under optimal capital control policy. The reason
is that, because of the distortions introduced by the combination of downward nominal wage
rigidity and a currency peg, aggregate dynamics can no longer be cast in terms of a Bellman
equation without introducing additional state variables. We therefore approximate the solu-
tion by policy function iteration over a discretized version of the state space (yTt , rt, dt, wt−1).
For details see Schmitt-Grohe and Uribe (2011a).
In approximating the aggregate dynamics of the economies with and without capital
controls, we discretize the endogenous dimensions of the state space using 501 equally spaced
points for the level of dt and 500 equally spaced points for the logarithm of wt−1.
4.1 Capital Controls During a Boom-Bust Episode
To illustrate the prudential nature of optimal capital controls in an economy undergoing a
currency peg, we simulate a boom-bust episode. We define a boom-bust episode as a situation
in which tradable output, yTt , is at or below trend in period 0, at least one standard deviation
above trend in period 10, and at least one standard deviation below trend in period 20. To
this end, we simulate the model economy for 20 million periods and select all subperiods
that satisfy our definition of a boom-bust episode. We then average across these episodes.
Figure 3 depicts the model’s predictions during a boom-bust cycle. Solid lines correspond
to the economy with free capital mobility and broken lines to the economy with optimal
capital controls. The two top panels of the figure display the dynamics of the two exogenous
driving forces, tradable output and the country interest rate. By construction, yTt and rt
are unaffected by capital controls. The middle left panel of the figure shows that capital
controls increase significantly during the expansionary phase of the cycle, from about 2
percent at the beginning of the episode to almost 7 percent at the peak of the cycle. During
the contractionary phase of the cycle, capital controls are drastically relaxed. Indeed at the
16
Figure 3: Prudential Policy For Peggers: Boom-Bust Dynamics With and Without CapitalControls
0 10 20 30 400.85
0.9
0.95
1
1.05
1.1
1.15
1.2Traded Output, yT
t
quarter
leve
l
0 10 20 30 406
8
10
12
14
16
18
20Annualized Interest Rate, rt
quarter
% p
er
ye
ar
0 10 20 30 40−2
0
2
4
6
8Capital Control Rate, τd
t
quarter
%
0 10 20 30 40−0.1
−0.05
0
0.05
0.1
0.15Trade Balance, yT
t − cTt
quarter
leve
l
0 10 20 30 400
5
10
15
20
25
30Unemployment Rate, 1− ht
quarter
%
0 10 20 30 400.75
0.8
0.85
0.9
0.95
1Consumption, ct
quarter
leve
l
No Capital Controls Optimal Capital Controls17
bottom of the crisis, capital inflows are actually subsidized at a rate of about 2 percent.
The sharp increase in capital controls during the expansionary phase of the cycle puts
sand in the wheels of capital inflows, thereby restraining the boom in consumption (see the
bottom right panel of figure 3). Under free capital mobility, during the boom, consumption
increases significantly more than under the optimal capital control policy. In the contrac-
tionary phase, the fiscal authority incentivates spending by subsidizing capital inflows. As
a result consumption falls by much less in the regulated economy than it does in the un-
regulated one. During the recession, the optimal capital control policy, far from calling for
austerity in the form of trade surpluses, facilitates large trade balance deficits as shown in the
middle right panel of figure 3. In this way, the capital control policy is able to stabilize the
absorption of tradable goods (not shown in figure 3) over the cycle. We note that the first-
best policy (which, as discussed earlier, could be implemented via an optimal exchange-rate
regime or with appropriate labor subsidies) calls not for running large deficits during crises,
but, on the contrary, for a trade surplus (see Schmitt-Grohe and Uribe, 2011a). This differ-
ence in the behavior of the trade balance highlights the fact that the second-best allocation
does not mimic the business cycle induced by the first-best allocation.
Because unemployment depends directly upon variation in the level of tradable absorption
through their role as a shifter of the demand schedule for nontradables, and because optimal
capital controls stabilize the absorption of tradables, unemployment is also stable over the
boom-bust cycle. Specifically, as can be seen from the bottom left panel of figure 3, in the
absence of capital controls, unemployment increases sharply by over 20 percentage points
during the recession. By contrast, under optimal capital controls the rate of unemployment
rises relatively modestly by about 3 percentage points.
Summarizing, the optimal capital control policy is prudential. It calls for restricting
capital inflows during booms and encouraging them during contractions. In this way, the
optimal capital control policy strengthens the role of the current account as a vehicle to
stabilize domestic absorption over the business cycle. Optimal government intervention
results in trade deficits during recessions and trade surpluses during booms of a much larger
scale than would occur under free capital mobility.
5 Level and Volatility Effects of Optimal Capital Con-
trols
Table 2 displays unconditional first and second moments of macroeconomic indicators of
interest for the economies with optimal capital controls and free capital mobility.
18
Table 2: Optimal Capital Controls: Level and Volatility Effects
Mean Standard DeviationOptimal No Optimal NoCapital Capital Capital Capital
Variable Symbol Controls Controls Controls ControlsCapital Control Rate τ d
t 2.4 0 5.2 0Unemployment Rate h − ht 3.1 13.5 7.6 11.7Consumption ct 0.97 0.89 0.08 0.10Trade Balance yT
t − cTt 0.05 0.11 0.12 0.07
Real Wage Wt/Et 2.1 2.3 0.6 0.7Traded Output yT
t 1.0 1.0 0.1 0.1Interest Rate rt 13.2 13.2 7.4 7.4External Debt dt 0.9 3.4 2.3 0.7Debt-to-Output Ratio dt/4/(y
T + ptcNt ) 11.2 26.0 22.1 12.6
Welfare Cost of Free Capital Mobility 9.1 percent of consumption
Note. τdt , h−ht, and dt/4/(yT
t +ptcNt ) are expressed in percent, rt is expressed in percent per year,
and ct, yTt − cT
t , Wt/Et, yTt , and dt are expressed in levels. The welfare cost of free capital mobility
is measured as the percent increase in consumption that the representative household living in the
economy with free capital mobility must receive every period to be unconditionally as well off as
living in the economy with optimal capital controls.
On average, the Ramsey planner imposes a positive tax on external debt of 2.4 percent.
This figure implies large average levels of capital controls, for the effective interest rate faced
by domestic debtors, given by (1 + rt)/(1 − τ dt ), increases from 13.2 percent per year under
free capital mobility to 24.8 percent per year under optimal capital controls. The main
reason why the Ramsey planner finds it optimal to impose capital controls on average is to
lower the average level of external debt holdings. We postpone an explanation of why this
is optimal until section 6.
Table 2 also shows that the tax on debt is highly volatile, with a standard deviation of 5.2
percentage points per quarter. The main payoff of imposing highly cyclical capital controls
is an enormous reduction in the average rate of unemployment from 13 percent under free
capital mobility to 3 percent under the optimal capital control policy. This reduction in
unemployment is welfare increasing because it raises the average level of production, and
hence also absorption, of nontradables, which provide utility to domestic households.
The reduction in unemployment is mediated by a significant reduction in the volatility
of the growth rate of tradable absorption. The standard deviation of the growth rate of
tradable consumption, cTt /cT
t−1, not shown in the table, falls from 5.3 percent under free
capital mobility to 2.9 percent under optimal capital controls. The connection between the
19
volatility of tradable consumption growth and unemployment follows from the fact that
consumption of tradables plays the role of a shifter of the demand for nontradables. In
turn, the Ramsey planner succeeds in curbing the variance of tradable expenditure growth
by raising the cost of external borrowing during booms and lowering it during recessions.
The correlation between traded output yTt and the capital control rate τ d
t is 0.54 and the
correlation between the interest rate rt and τ dt is -0.58. Furthermore, the Ramsey planner
engineers an effective interest rate that is positively correlated with traded output in spite
of the fact that the interest rate itself is highly negatively correlated with the latter.
Table 2 shows that the first and second moments of the real (and nominal) wage rates
are not significantly affected by the presence of capital controls. This prediction of the
model might appear as surprising because downward wage rigidity is the sole friction in
the present model, and because unemployment behaves markedly differently across capital
control regimes. A reason why the unconditional moments of real wages are so similar in the
two regimes is that the lower bound on wages is binding most of the time in both economies
(85 percent of the time under free capital mobility and 65 percent of the time under optimal
capital controls), and, when this happens, the wage rate falls at the common gross rate γ.
A reason why the first and second moments of unemployment are so different across regimes
in spite of the similarity in the corresponding moments of real wages is that when the wage
constraint is binding the magnitude of the unemployment rate depends on the strength of
the domestic absorption of tradables, which is significantly different across regimes.
An important distinction in wage dynamics across capital control regimes that is not
captured by the unconditional moments shown in table 2 is the behavior of wages during
booms. During economic expansions, the Ramsey fiscal authority, through capital controls,
limits the appreciation of real wages. In this way, it also reduces the need for large decreases
in the real wage once the boom is over. To visualize the role of optimal capital controls in
limiting wage increases during booms, figure 4 displays the cumulative probability distribu-
tion of positive wage changes under free capital mobility and under optimal capital controls.
Under optimal capital controls the vast majority of wage increases are small. Specifically,
90 percent of wage increases are less than 5 percent in magnitude. By contrast, only about
half of all wage increases that occur under free capital mobility are smaller than 5 percent.
This difference underlines the prudential nature of optimal capital controls.
6 Peg-Induced Overborrowing
Table 2 shows that the average level of external debt in the economy with free capital mobility
is more than three times higher than it is in the economy with optimal capital controls.
20
Figure 4: Cumulative Probability Distribution of Positive Wage Changes
5 10 15 20 25 300.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Cum
ula
tive P
robabili
ty D
ensity
Wage Growth (%)
Free Capital Mobility
Optimal Capital Controls
This prediction of the model is also evident from figure 5, which shows the unconditional
distribution of external debt under free capital mobility (solid line) and under optimal capital
controls (dashed line). The Ramsey planner induces a lower average level of external debt
by taxing borrowing at a positive rate. Recall that the average tax rate on debt is 2.4
percent per quarter. It follows that pegging economies with free capital mobility accumulate
inefficiently large amounts of external debt. In other words currency pegs in combination
with free capital mobility lead to overborrowing.
The reason why the average level of external debt is lower under optimal capital controls
than under free capital mobility is that the Ramsey planner finds it optimal to induce an
external debt position that is significantly more volatile than the one associated with free
capital mobility. As shown in table 2, the standard deviation of external debt is 2.3 under
optimal capital controls, but only 0.7 under free capital mobility. Similarly, figure 5 shows
that the distribution of external debt is significantly more dispersed under optimal capital
controls than under free capital mobility. A more volatile process for external debt requires
centering the debt distribution further away from the natural debt limit, for precautionary
reasons. In turn, the reason why the Ramsey planner finds wide swings in the external debt
position desirable is that such variations allow him to insulate the domestic absorption of
tradable goods from exogenous disturbances buffeting the economy. Put differently, in the
Ramsey economy, external debt plays the role of shock absorber to a much larger extent
21
Figure 5: The Distribution of External Debt
−6 −4 −2 0 2 4 6 80
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
External Debt (level)
Density
Free Capital Mobility
Optimal Capital Controls
that it does in the economy with free capital mobility.
7 Welfare Costs of Free Capital Mobility for Peggers
We have established that in the present economy, free capital mobility entails excessive
external debt and unemployment. Both of these factors tend to depress consumption and
therefore reduce welfare. In this section, we quantify the welfare losses associated with free
capital mobility in economies subject to a currency peg.
We define the welfare cost of free capital mobility, denoted λ, as the permanent percent
increase in the lifetime consumption stream required by an individual living in the economy
with free capital mobility to be unconditionally as well off as an individual living in the
economy with optimal capital controls. Formally, λ is implicitly given by
E
∞∑
t=0
βtU(cFCMt (1 + λ)) = E
∞∑
t=0
βtU(cOCCt ),
where cFCMt and cOCC
t denote, respectively, consumption in the economy with free capital
mobility and consumption in the economy with optimal capital controls in period t.
Table 2 shows that the welfare cost of free capital mobility for a pegging economy is
22
enormous. The representative household living in the economy with free capital mobility
requires an increase of 9.1 percent in consumption every period to be indifferent between
living under free capital mobility and living under optimal capital controls. Thus, the present
model speaks with a strong voice against allowing capital to flow freely across borders in
economies with fixed exchange rates and downwardly rigid wages.
8 Greece and Spain
In this section we investigate the sensitivity of our main results to changes in the exogenous
driving process. Specifically, we estimate the law of motion of traded output and the country
interest rate using quarterly data from two peripheral European countries, Greece and Spain
over the period 1980-2011. The appendix describes the data sources. The estimates of
A, Σν , and r defining the exogenous bivariate first-order autoregressive processes given in
equation (28) are
A =
[
0.88 −0.42
−0.05 0.59
]
; Σν =
[
0.000536 −0.000010
−0.000010 0.000060
]
; r = 0.011.
for Greece and
A =
[
0.95 0.04
0.01 0.78
]
; Σν =
[
0.000134 −0.000000
−0.000000 0.000046
]
; r = 0.0123.
for Spain. Table 3 displays some features of the process [yTt rt]
′ implied by our estimates.
Both Greece and Spain face lower interest rates than Argentina. The average value of rt is
about 5 percent for Greece and Spain and over 13 percent for Argentina. In addition, the
two European economies face smaller external shocks. The estimated volatilities of tradable
output and the interest rate in these two countries are significantly lower than their Argentine
counterparts. The reduced level of external uncertainty lowers precautionary savings, and
the lower average real interest rate makes external borrowing more attractive. As a result, as
shown in the table, the average long-run debt-to-output ratio implied by the model is much
higher under the exogenous processes estimated on Greek and Spanish data than under the
one estimated on Argentine data.
Lower uncertainty and higher levels of external debt have opposite effects on the welfare
costs of capital mobility for peggers. On the one hand, all other things equal, less uncertainty
makes free capital mobility less costly for peggers. On the other hand, as we show elsewhere
(Schmitt-Grohe and Uribe, 2011b), a higher level of external debt increases the welfare cost
23
Table 3: Model Implications Using Data From Greece and Spain
Statistic Argentina Greece SpainInterest Rate (% yr.)Mean 13.2 4.5 5.1Standard Deviation 7.4 5.2 4.7
Traded Output, yTt (% dev. from trend)
Standard Deviation 12.3 6.5 3.6Corr(yT
t , rt) -0.86 -0.62 0.13Capital Control Rate, τ d
t (% qtr.)Mean 2.4 3.3 3.4corr(τ d
t , yTt ) 0.54 0.49 0.18
corr(τ dt rt) -0.58 -0.49 -0.56
Mean Unemployment (%)Free Capital Mobility 13.5 15.3 10.8Optimal Capital Controls 3.1 3.8 2.2
Std. Dev. Consumption (%)Free Capital Mobility 12.5 16.1 12.1Optimal Capital Controls 9.6 10.6 7.3
Debt-to-Output Ratio (%)Free Capital Mobility 26 113 162Optimal Capital Controls 11 99 152
Welfare Cost of Free Capital Mobility
(% of consumption) 9.2 13.4 9.2
of free capital mobility for peggers. In the case of Greece, for example, even though the level
of uncertainty is lower than that of Argentina, the welfare cost of free capital mobility turns
out to be higher than in Argentina. The reason is that the level of external debt induced
by the exogenous driving process fit to Greek data is much higher than that induced by the
process estimated with Argentine data.
The welfare cost of free capital mobility estimated for Spain is significantly smaller than
that estimated for Greece even though the implied external debt level for the former is
much higher. We attribute this result to the fact that the Greek interest rate is strongly
countercyclical whereas the Spanish interest rate is mildly procyclical. Using the terminology
coined by Kaminsky et al. (2005), when it rains in Greece it pours, whereas it does not in
Spain.
24
9 Conclusion
The first contribution of this paper is to identify a negative pecuniary externality afflicting
economies with downward nominal wage rigidity and fixed exchange rates. In this type of
economic environment, private absorption expands too much in response to favorable shocks,
causing inefficiently large increases in real wages. No problems are manifested in this phase
of the cycle. However, as the economy returns to its trend path, wages fail to fall quickly
enough because they are downwardly rigid. In addition, the central bank, having its hands
tied by the commitment to a fixed exchange rate, cannot deflate the real value of wages via
a devaluation. In turn, high real wages and a contracting level of aggregate absorption cause
involuntary unemployment. Individual agents are conscious of this mechanism, but are too
small to internalize it. The government, on the other hand, does internalize the distortion
and therefore has an incentive to intervene.
The second contribution of the present study is to analyze the ability of capital con-
trols to ameliorate the distortions introduced by the peg-induced pecuniary externality. We
characterize both analytically and numerically the Ramsey optimal capital control policy.
We show that, although capital controls cannot bring about the first-best allocation, they
go a long way toward easing the pains of pegs. Under plausible calibrations of our model,
we find that the representative household living in the economy with free capital mobility
requires a 9.1 percent permanent increase in consumption to be unconditionally indifferent
between continuing to live in that environment and migrating to one with optimally set
capital controls.
The third contribution of the present investigation is to establish that the optimal capital
control policy is prudential in nature. The benevolent government taxes capital inflows
in good times and subsidizes external borrowing in bad times. As a result, the economy
experiences trade surpluses during booms and deficits during recessions. The key role of
capital controls is to insulate the domestic absorption of tradable goods from external shocks.
In this way, the government avoids that external disturbances spill over into the nontraded
sector where they would otherwise cause unemployment.
The fourth important finding of our inquiry is to establish that pegging economies are
prone to overborrowing. In our calibrated model, the average debt-to-output ratio falls from
26 percent in the economy with free capital mobility to 11 percent in the economy with
optimal capital controls. The regulated economy accumulates a war chest of assets (or a
reduced level of debt) in order to be able to stabilize traded consumption when the economy
is buffeted by negative external shocks.
In summary, the results of the present study strongly suggest that, when labor markets
25
suffer from downward nominal wage rigidity, fixed exchange rate arrangements should not
be coupled with free capital mobility. On the contrary, in such economies, capital controls
can be a highly effective instrument for macroeconomic stabilization. More importantly, the
predictions of our model suggest that governments of fixed-exchange-rate economies should
concentrate effort not on crisis management, but rather on crisis prevention.
26
Appendix: Data Description
In this appendix, we report the estimate of the exogenous driving process [yTt rt]
′ for the
cases of Greece and Spain. We also describe how the empirical measures of yTt and rt were
constructed.
Greece
The estimation uses quarterly data from 1981:Q1 to 2011:Q3. Greece did not produce
sectoral GDP data between 1991 and 1999. For this reason, we proxy traded output by
an index of industrial production. Specifically, we use the index of total manufacturing
production 2005=100 from the OECD seasonally adjusted at the source. The original series
begins in 1955:Q1 and ends in 2011:Q3. We removed a cubic trend from the natural logarithm
of the index over the period 1955:Q1 to 2011:Q3. We use observations of the detrended series
for the period 1981:Q1 to 2011:Q3 to make the range compatible with the one corresponding
to the country real interest rate.
It is also difficult to obtain a consistent measure of the Greek real interest rate over the
past three decades. The reason is twofold. First, JP Morgan does not produce the EMBI
index for Greece. Second, we were unable to find an interest rate for a constant maturity
instrument over the whole sample. In face of these data limitations, we proceed as follows.
We measure the real interest rate in terms of tradables using the formula
1 + rt = (1 + it)Et
[
EtPT ∗
t
Et+1P T ∗
t+1
]
,
where rt denotes the real country interest rate in terms of tradables, it denotes the nominal
interest rate in terms of national currency, Et denotes the nominal exchnage rate defined
as units of domestic currency per unit of ECU or Euro as applicable (Greece’s legal tender
changed to the Euro in 2001), P T ∗
t denotes the foreign-currency price of tradables, and Et
denotes the expectations operator conditional on information available in period t. This
formula assumes that the marginal rate of substitution is uncorrelated with the inverse
of the domestic rate of inflation of tradable goods. The source for Et is Eurostat (code
ert_h_eur_q). We measure P T ∗
t by the German consumer price index published by the
OECD. We measure it as follows. For the period 1981:Q1 to 1992:Q3 it is the overnight
interest rate published by the Bank of Greece. For the period 2001:Q1 to 2011:Q3 we
proxy it by the interest rate on 10-year Greek treasury bonds published by Eurostat (code
irt_lt_mcby_q). For the period 1992:Q4 to 2000:Q4, we measure it as the average of the
above two interest rates. We proxy Et
[
EtPT∗
t
Et+1PT∗
t+1
]
by the one-period ahead forecast ofEtP
T∗
t
Et+1PT∗
t+1
27
implied by an estimated AR(2) process for this variable. We discretize the driving process
following the same procedure described in the body of the paper for the case of Argentina.
Spain
The estimation of the driving process uses quarterly data over the period 1980:Q3 to 2011:Q4.
We proxy tradable output by the sum of sectorial GDP in agriculture, livestock breeding,
forestry, fishing, and industry net of construction at constant prices of 1995. The source
is INE (www.ine.es). The average share of tradables in GDP over the estimation sample
is 26 percent. The logarithm of traded GDP is detrended by removing a cubic time trend.
The procedure for constructing the Spanish real interest rate is similar to that emplyed
for Greece, except that here we measure the nominal interest rate by the 10-year Spanish
treasury bond published by Eurostat under the name EMU convergence criterion bond yields
(code irt_lt_mcby_q).
28
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